CN114400892A - Digital optimal time dynamic control method of Boost converter - Google Patents

Digital optimal time dynamic control method of Boost converter Download PDF

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CN114400892A
CN114400892A CN202210035478.2A CN202210035478A CN114400892A CN 114400892 A CN114400892 A CN 114400892A CN 202210035478 A CN202210035478 A CN 202210035478A CN 114400892 A CN114400892 A CN 114400892A
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load
output voltage
current
switching tube
boost converter
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CN114400892B (en
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陈章勇
刘海峰
陈勇
肖方波
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University of Electronic Science and Technology of China
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M3/00—Conversion of dc power input into dc power output
    • H02M3/02—Conversion of dc power input into dc power output without intermediate conversion into ac
    • H02M3/04—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters
    • H02M3/10—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M3/145—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M3/155—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
    • H02M3/156—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators
    • H02M3/157—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators with digital control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/08—Circuits specially adapted for the generation of control voltages for semiconductor devices incorporated in static converters
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B70/00—Technologies for an efficient end-user side electric power management and consumption
    • Y02B70/10—Technologies improving the efficiency by using switched-mode power supplies [SMPS], i.e. efficient power electronics conversion e.g. power factor correction or reduction of losses in power supplies or efficient standby modes
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/50—Photovoltaic [PV] energy
    • Y02E10/56—Power conversion systems, e.g. maximum power point trackers

Abstract

The invention aims to provide a digital optimal time dynamic control method of a Boost converter, belonging to the technical field of power electronics. The method divides the working state of the Boost converter into two conditions for different control: during the transient period, an SOTDC method is adopted for control, namely, the on-off time of a switching tube is estimated by using state plane analysis, and the duty ratio of a driving signal is changed to enable a state variable to reach a target working point in the shortest time; in a steady state process, an improved Active Disturbance Rejection Control (ADRC) control method is adopted to reduce the influence of the zero point of the right half plane in the converter on the system. The method can significantly improve dynamic response while maintaining closed loop stability.

Description

Digital optimal time dynamic control method of Boost converter
Technical Field
The invention belongs to the technical field of power electronics, and particularly relates to a digital optimal time dynamic control method of a Boost converter.
Background
Over the past several decades, DC-DC converters have been developed in great numbers and are used in a wide variety of applications, such as photovoltaic systems, fuel cells, hybrid vehicles, etc. However, some converters in DC-DC converters are non-minimum phase (NMP) systems, such as Boost converters and buck-Boost derived converters, i.e., converters that control the transfer function of the input duty cycle to the output voltage to have a right half-plane zero. The variator with the NMP system causes a large phase angle lag between its output and input, resulting in a slow system response. If changes in the converter parameters (i.e., load resistance and voltage gain), such as a decrease in input voltage or load resistance, cause the right half-plane zero to move toward the origin, the NMP problem is further exacerbated by the dynamic shift of the positive zero position, resulting in system instability.
The current methods for solving the non-minimum phase problem can be roughly divided into two categories: one is the technical goal of achieving minimum phase dynamics by designing the converter topology, while this performance improvement achieved by designing the topology is very significant in heavy load and high voltage gain applications where the right half-plane zero is located very close to the origin, the additional components (switches, inductors and capacitors) required in the new topology add complexity and cost to the implementation; another is to improve system performance by designing control methods for non-minimum phase systems.
Currently, the following control methods are commonly used in the prior art: 1. typical boundary control method based on variable structure of sliding mode[1][2]In this control method, the state variables are moved without restriction until the sliding surface is reached; and then, the Boost converter is continuously switched between an on structure and an off structure to force the working point to follow the sliding mode surface and reach a target working point after a plurality of switch actions. Compared with the traditional linear control, the variable structure control based on the sliding mode can achieve enhanced dynamic response, but high-frequency vibration caused by the method on the switch surface is difficult to eliminate, unmodeled dynamic state of the system is easy to excite, and the system can be unstable. 2. Multi-loop current mode control method[3]The input inductor current is regulated by an inner current loop with a high crossover frequency and the output voltage is regulated by a slower outer voltage loop, and the design of this control method takes into account different loop gains and specific target operating points to evaluate system performance. But because the dynamic behavior of the Boost converter depends onThe power supply and the load are input, so that the dynamic and steady-state performance of the design parameters based on the multi-loop current mode control method is poor when the power supply or the load has large disturbance. 3. There are other proposed control schemes for Boost converters, such as proportional-integral control based on a reduced order observer applied to voltage control of Boost converters[4]The bandwidth limitation imposed by the right half-plane zero point of the minimum phase system is defined; and introducing a plane filtering algorithm as a robust extension of a Generalized Proportional Integral (GPI) controller[5]The method is used for jointly attenuating the influence of internal and external disturbance changing along with time in a voltage tracking scene. These control methods rely heavily on accurate mathematical models or deep understanding of the input-output relationships of the circuit topology, however, obtaining accurate models and accurate parameter values for the system is often difficult to achieve.
[1]R.Munzert and P.T.Krein,“Issues in boundary control,”in Proc.IEEE Power Electron.Spec.Conf.,Baveno,Italy,Jun.1996,pp.810–816.
[2]M.Greuel,R.Muyshondt,and P.T.Krein,“Design approaches to boundary contr ollers,”in Proc.IEEE Power Electron.Spec.Conf.,St.Louis,Missouri,USA,Jun.1997,pp.672–678.
[3]R.Ridley,B.Cho,and F.Lee,“Analysis and interpretation of loop gains of multi loop-controlled switching regulators,”IEEE Trans.Power Electron.,vol.3,no.4,pp.489–498,Oct.1988.
[4]Alvarez-Ramirez,J.,Cervantes,I.,Espinosa-Perez,G.,et al.:‘A stable design of PI control for DC–DC converters with an RHS zero’,IEEE Trans.Circuits Syst.I,Fun dam.Theory Appl.,2001,48,(1),pp.103–106
[5]Linares-Flores,J.,Mendez,A.H.,Garcia-Rodriguez,C.,et al.:‘Robust nonlinear a daptive control of a‘boost’converter via algebraic parameter identification’,IEEE Trans.Ind.Electron.,2014,61,(8),pp.4105–4114
Disclosure of Invention
Aiming at the problem of poor transient performance of a system in a non-minimum phase system control method in the background art, the invention provides a digital optimal time dynamic control method (SOTDC) of a Boost converter. The method divides the working state of the Boost converter into two conditions for different control: during the transient period, an SOTDC method is adopted for control, namely, the on-off time of a switching tube is estimated by using state plane analysis, and the duty ratio of a driving signal is changed to enable a state variable to reach a target working point in the shortest time; in a steady state process, an improved Active Disturbance Rejection Control (ADRC) control method is adopted to reduce the influence of the zero point of the right half plane in the converter on the system. The method can significantly improve dynamic response while maintaining closed loop stability.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a digital optimal time dynamic control method of a Boost converter comprises the following steps:
step 1, judging whether the circuit is in a steady state or a transient state, and if the circuit is in the transient state, executing step 2; otherwise, executing step 5;
step 2, judging whether the load changes from heavy load to light load or from light load to heavy load, and if the load changes from light load to heavy load, executing the step 3; otherwise, executing step 4; the change from heavy load to light load is that the load current at the next moment is reduced compared with the load current at the current moment;
step 3, when the load jumps from light load to heavy load, at tonIn the period, the switching tube is switched on, the duty ratio is 100 percent, and at toffThe switching tube is turned off in the period, the duty ratio is 0%, and the shortest recovery time for the output voltage to reach the steady state again is tMRT，tMRT＝ton+toff；
wherein ,
Figure BDA0003468169380000031
in the above formula, Ion3For a load current at a known desired target operating point under heavy load iLn2The inductor current at the transient point, von2Output voltage at transient point, Vccn is normalized input voltage, iLntInductor current for heavy-duty operating points, iLn(0) The initial inductive current at the light load working point;
step 4, when the load jumps from heavy load to light load, at tonIn the period, the switching tube is switched on, and the duty ratio of the driving signal is 100%; at toffDuring the period, the switching tube is turned off, the duty ratio of the driving signal is 0%, and the shortest recovery time for the output voltage to reach the steady state again is tMRT，tMRT＝ton+toff，
wherein ,
Figure BDA0003468169380000032
in the above formula, iLn(0) For the initial value of the inductance current at the heavy-duty working point, iLntThe inductance current value V at the expected target operating point known during light loadccIs an input voltage vonAOutput voltage value v at inductor current 0 for turn-off traceonBOutput voltage value i at inductor current 0 for switching on traceon2Is the load current at the transient point;
and step 5, when the circuit is in a steady state, using an improved active disturbance rejection controller for control, wherein the active disturbance rejection controller is specifically,
Figure BDA0003468169380000033
in the above formula, k1 and k2For the controller gain, yrefIn order to achieve the desired output voltage,
Figure BDA0003468169380000034
respectively the output voltage and the inverse output voltage observed by the extended observer, b0In order to control the coefficients of the input,
Figure BDA0003468169380000035
is the estimated perturbation.
Further, the topology of the Boost converter includes: an inductor (L), a capacitor (C), a switch tube (S1) and a diode (D1); the drain electrode of the switching tube (S1) is connected with one end of the inductor, and the source electrode of the switching tube (S1) is connected with the negative electrode of the input power supply; the anode of the diode (D1) is connected with one end of the inductor and the drain of the switch tube (S1), the cathode of the diode (D1) is connected with one end of the output capacitor (C), and the other end of the output capacitor (C) is connected with the negative electrode of the power supply.
Further, the output voltage of the Boost converter cannot be negative due to the presence of diodes in the circuit topology.
Further, the operation mode of the Boost converter during the steady state is a Continuous Conduction Mode (CCM).
Further, the control method is suitable for the condition that the load disturbance is small, namely the disturbance enables the output voltage of the converter to be not 0.
Further, the controller gain k1＝wc 2,k2＝2wc，wcA controller gain parameterized for bandwidth.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
1. according to the transient control method based on the natural track, when the load is disturbed, the on track and the off track of the transient control method are known, so that when the load is disturbed, the dynamic response process of the transient control method is operated based on the natural state change track, the minimum recovery time is realized by respectively calculating the on time and the off time of the MOSFET switching tube, the dynamic response of the system is improved, and the output of the Boost converter can quickly follow the expected voltage.
2. The ADRC controller improved by designing the filter obtains better compromise between dynamic response and closed-loop bandwidth. The presence of the zero point Z of the right half-plane results in a closed-loop bandwidth w of the systemclIs limited to wcl< z/2, indirectly resulting in observer bandwidth also being limited below closed loop bandwidth; after the filter is designed, the bandwidth of the observer is increased, and the increase of the closed-loop bandwidth is indirectly reflected, so that the dynamic response capability of the system is enhanced.
Drawings
FIG. 1 is a simplified circuit schematic of a Boost converter;
wherein, (a) is a topological structure chart; (b) turning on an equivalent circuit diagram for the switching tube; (c) the equivalent circuit diagram is the turn-off circuit diagram of the switching tube.
Fig. 2 is a normalized trace diagram of the turn-on and turn-off of the MOSFET of the switching tube in the Boost converter.
Fig. 3 is a block diagram of the control method of the present invention.
FIG. 4 is a simplified optimal time dynamics control diagram of the present invention when the load is from light load to heavy load;
wherein, (a) is a phase trace diagram of output voltage and inductive current, (b) is an output voltage waveform, and (c) is an inductive current waveform.
FIG. 5 is a simplified optimal time dynamics control diagram of the present invention when the load is from heavy load to light load;
wherein, (a) is a phase trace diagram of output voltage and inductive current, (b) is an output voltage waveform, and (c) is an inductive current waveform.
Fig. 6 is a block diagram of an improved ADRC controller according to the present invention.
FIG. 7 is a simulation diagram of the output voltage of the present invention based on the digital optimal time dynamic control when the load is changed from light load to heavy load.
FIG. 8 is a simulation diagram of the output voltage of the present invention based on the digital optimal time dynamic control when the load is from heavy load to light load.
FIG. 9 is a simulation diagram of the variation of the waveform of the inductor current when the control method of the present invention is applied during the jump of the load;
wherein, (a) is a simulation diagram of the inductor current from light load to heavy load; (b) the simulation diagram of the inductor current is from heavy load to light load.
Fig. 10 is a waveform diagram of a simulation of a conventional active disturbance rejection control.
Wherein, (a) is a light load to heavy load output voltage simulation diagram; (b) the voltage simulation diagram is output for heavy load to light load.
Fig. 11 is a simulated waveform diagram of the combination of the conventional active disturbance rejection control and the digital-based optimal time dynamic control of the present invention.
Wherein, (a) is a light load to heavy load output voltage simulation diagram; (b) the voltage simulation diagram is output for heavy load to light load.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the following embodiments and accompanying drawings.
The control method of the invention is designed for a Boost converter with a non-minimum phase (NMP) system, and the simplified circuit schematic diagram of the Boost converter is shown in fig. 1. The circuit topology structure is as shown in fig. 1(a), and includes: an inductor (L), a capacitor (C), a switch tube (S1) and a diode (D1); the drain electrode of the switching tube (S1) is connected with one end of the inductor, and the source electrode of the switching tube (S1) is connected with the negative electrode of the input power supply; the anode of the diode (D1) is connected with one end of the inductor and the drain of the switch tube (S1), the cathode of the diode (D1) is connected with one end of the output capacitor (C), and the other end of the output capacitor (C) is connected with the negative electrode of the power supply; the output capacitor (C) is connected with the load (R) in parallel. Fig. 1(b) and fig. 1(c) are equivalent circuit diagrams of switching on or off of the switching tube MOSFET, respectively. When the switch tube MOSFET is switched on, the inductor current stores energy, and when the switch tube MOSFET is switched off, the energy stored in the inductor is transmitted to the load.
For the above-described transformer, in order to eliminate the dimension of the state variable to obtain generality, the variable is subjected to normalization processing,
Figure BDA0003468169380000051
wherein ,VrIs a reference voltage, foIn order to be the natural frequency of the frequency,
Figure BDA0003468169380000052
l and C are respectively inductance and capacitance, ZoIn order to be the characteristic impedance,
Figure BDA0003468169380000053
when the switching tube is turned on (u is 1) and turned off (u is 0) (u refers to the state of the MOSFET switching tube and is also the control input of the system), according to KCL and KVL law, the state equation of the inductor current and the output voltage is as follows,
Figure BDA0003468169380000054
Figure BDA0003468169380000055
wherein ,VccIs the input voltage iLIs the inductive current, voIs the output voltage;
assuming that no power loss occurs during the operation of the Boost converter, the input power is equal to the output power, and the load line is defined as follows:
Figure BDA0003468169380000061
when the target operating voltage (output voltage equal to desired voltage) is normalized, the result is von,target＝1，
Figure BDA0003468169380000062
The target operating point of the converter is (v)on,target,iLn,target) The determination can be made according to (3) and (4).
Obtaining the phase tracks of the normalized inductive current and the output voltage by the ordinary differential equation when the switching tube is switched on and off at the target working point:
Figure BDA0003468169380000063
when u is 0, the phase locus of the inductor current and the output voltage is (V)ccn,ion) As a circle center, with a desired working point
Figure BDA0003468169380000064
To the center of a circle (V)ccn,ion) A circle with a radius; and when u is 1, the phase locus of the inductance current and the output voltage is a passing point
Figure BDA0003468169380000065
Has a slope of
Figure BDA0003468169380000066
Is measured. As shown in fig. 2, the switching-on and switching-off tracks of the Boost converter are tangent at the target working point, and ideally, when the system reaches a steady state, the Boost converter performs high-frequency switching-on and switching-off near the target working point.
If the output voltage cannot be negative, and the Boost converter operates in Continuous Conduction Mode (CCM) during steady state.
A digital optimal time dynamic control method of a Boost converter is shown in a structural block diagram of fig. 3 and comprises the following steps:
step 1, judging whether the circuit is in a steady state or a transient state, and if the circuit is in the transient state, executing step 2; otherwise, executing step 5; when the load current jumps, the transient state is entered, the transient state is ended, and the steady state is entered;
step 2, judging whether the load changes from heavy load to light load or from light load to heavy load, and if the load changes from light load to heavy load, executing the step 3; otherwise, executing step 4; if the load is disturbed, the load current at the next moment is increased compared with the load current at the current moment, namely the load is heavy, otherwise, the load is light;
step 3, when the load jumps from light load to heavy load, at tonIn the period, the switching tube is switched on, and the duty ratio is 100%; at tofThe switching tube is turned off in the period, the duty ratio is 0%, and the shortest recovery time for the output voltage to reach the steady state again is tMRT，tMRT＝ton+toff wherein ,
Figure BDA0003468169380000071
the specific process is shown in figure 4,
fig. 4 is a simplified optimal time dynamics control diagram for a load from a light load to a heavy load, where point 3 is a known expected target operating point for the heavy load, so the turn-on and turn-off trajectories at point 3 for the heavy load are:
Figure BDA0003468169380000072
Figure BDA0003468169380000073
when v isonWhen the value is 0; the inductor currents on the turn-on and turn-off traces are respectively:
Figure BDA0003468169380000074
Figure BDA0003468169380000075
as shown in fig. 4(a), when the load changes from a light load to a heavy load, at the initial time, the operating point is at 1, and the target operating point moves from 1 to 3 due to the increase of the load current; and the energy stored in the inductor is not enough to supply the output filter capacitor and the load at the initial moment, so the switch is switched on at the initial moment, the switching-on time is determined by the load change, and when the load has large disturbance (i)LnA＜iLnB) When the output voltage enters discontinuous mode and the load has small disturbance (i)LnA≥iLnB) The output voltage will enter a continuous mode;
under the condition of subsequent known circuit parameters and under the condition that the output voltage is 0, the inductance current values of the turn-on and turn-off tracks are calculated, and the output voltage is found not to enter a discontinuous mode when disturbance occurs when the output voltage jumps from light load to heavy load. At this time, in order to obtain the minimum recovery time, the operating point follows the trajectory λonUntil it ends at point 2, at which time t12nIs an inductive current charging stage; then, the switching tube is turned off, and the operating state follows the trajectory λ from the operating point 2offPointing to the target operating point 3, covering an angle (beta)2α), at this time t23nIs the discharge phase of the inductor current.
Fig. 4(b) and fig. 4(c) show the variation traces of the output voltage and the inductor current during the transition from the light load to the heavy load, respectively, and the specific calculation method is as follows:
the inductor current and the output voltage at the operating point 1 are known expected operating points at light load, the turn-on trajectory λ from point 1 to point 2onThe linear equation of (a) is:
Figure BDA0003468169380000076
simultaneous equations 7 and 10 find the coordinates of point 2
Figure BDA0003468169380000081
Figure BDA0003468169380000082
wherein ：
Figure BDA0003468169380000083
obtaining a loading transient (t) by performing a geometric analysisMRT)
Figure BDA0003468169380000084
wherein ,
Figure BDA0003468169380000085
Figure BDA0003468169380000086
therefore, when the load jumps from a light load to a heavy load, at tonThe switch tube is on in the period, the duty ratio is 100 percent; at toffIn the period, the switching tube is turned off, and the duty ratio is 0%. The lowest recovery time for the output voltage to reach steady state again is tMRT；
Step 4, when the load jumps from heavy load to light load, at tonIn the period, the switching tube is switched on, and the duty ratio is 100%; at toffThe switching tube is turned off in the period, the duty ratio is 0%, and the shortest recovery time for the output voltage to reach the steady state again is tMRT，tMRT＝ton+toff；
wherein ,
Figure BDA0003468169380000087
toff＝t12n+t22'n，
Figure BDA0003468169380000088
Figure BDA0003468169380000089
the specific process is as follows:
fig. 5 is a simplified optimal time dynamic control diagram of the present invention when the load is from heavy load to light load, and the operating point 3 is a known expected target operating point when the load is light load, so the on and off traces of the operating point are respectively:
Figure BDA00034681693800000810
Figure BDA0003468169380000091
at a known desired operating point when the inductor current and the output voltage at the operating point 1 are heavy, the off-trace λ from point 1 to point 2offThe linear equation of (a) is:
Figure BDA0003468169380000092
when i isLnWhen equal to 0The output voltages on the turn-on and turn-off traces are respectively:
Figure BDA0003468169380000093
Figure BDA0003468169380000094
during load step-down, in order to obtain a minimum recovery time, it is assumed that the switching tube is immediately turned off when load step-down occurs at the initial point 1. The state of the converter starts to follow the trajectory λoffAnd (4) changing. The turn-off time is determined by the magnitude of the load change, and the load enters a discontinuous mode (v) when a large disturbance inductive current appearsonA＞vonB) And the inductor current enters a continuous mode (v) when the load has small disturbanceonA≤vonB)。
Under the condition that the known circuit parameters and the inductive current are 0, the output voltage values of the turn-on and turn-off tracks are calculated, and the inductive current is found to enter a discontinuous mode when large disturbance inductive current occurs when the inductive current jumps from heavy load to light load. As shown in fig. 5 (a). At this time, in order to obtain the minimum recovery time, the operating point follows the trajectory λoffUntil it ends at point 2', at which time t12'nIs an inductive current charging stage; then, the switch tube is turned on, and the working state follows the track lambda from the working point 2onPoint to the target operating point 3, at this time t2'3nIs the discharge phase of the inductor current.
Fig. 5(b) and 5(c) show the variation traces of the output voltage and the inductor current during the transition from the heavy load to the light load, respectively, and the specific calculation method is as follows:
the value i of the inductance current at the final moment of the known turn-on trackLnBWhen the switching tube is turned on, the time can be calculated as:
Figure BDA0003468169380000095
the turn-off time of the switching tube is divided into two parts, one part is an inductive current continuous part t12nAnd a part of the inductor current discontinuous part t22'nThe two part times are calculated as follows:
Figure BDA0003468169380000096
wherein ：
Figure BDA0003468169380000101
Figure BDA0003468169380000102
and at t22'nIn the time period, the inductive current is in a discontinuous mode, the output capacitor supplies power to the load, and in the process, the load current is approximately considered to be constant and is ion2Since the voltage fluctuation is not large at the time of load disturbance, the output voltage is approximately considered to be equal to the desired voltage, so that the load current is considered to have a small fluctuation in change after the load has a step disturbance. At this time according to
Figure BDA0003468169380000103
Obtaining:
Figure BDA0003468169380000104
then, the total off-time is:
toff＝t12n+t22'n (22)
so that when the load is changed from heavy load to light load, at tonIn the period, the switching tube is switched on, and the duty ratio is 100%; at toffIn the period, the switching tube is turned off, and the duty ratio is 0%.
Step 5, when the circuit is in a steady state, because the voltage dynamic of the boost converter has inverse response, oneNormally, the right half-plane zero point zRHPFor closed loop bandwidth wclThe limitations of (2) are: w is acl＜zRHPAnd/2, which also causes that the traditional linear control is difficult to produce better control effect. The closed-loop bandwidth of the non-minimum phase system is limited by the right half-plane zero, the right half-plane zero in the disturbance part is separated by combining the pole information on the basis of a traditional Active Disturbance Rejection Control (ADRC) controller of the extended state observer, and a filter is designed to reduce the influence of the right half-plane zero in the boost converter on the system, namely, the control is carried out through the improved active disturbance rejection controller, the circuit structure block diagram of which is shown in figure 6, obtaining an observation equation of an extended observer (ESO) according to an output equation of a controlled object (Boost converter), wherein the ESO respectively observes three values of output voltage, an output voltage derivative and partial disturbance, and the other part of the disturbance related to the right half plane zero point is separated and then passes through a low-pass filter, so that the non-minimum phase link phenomenon is improved, and finally, the control input u of the low-pass filter is obtained according to the PD control and the disturbance value. In the figure, yrefRepresenting the desired output voltage, y being the output voltage, boIs a coefficient of the control input u, b1Is the coefficient controlling the derivative of the input u, c is the time constant of the low-pass filter, z1,z2,z3Respectively are observed values of the output voltage, the derivative of the output voltage and partial disturbance; the controller is a PD controller, the plant is a controlled object, and the Extended State observer is an Extended State observer;
the specific design process of the active disturbance rejection controller comprises the following steps:
the dynamic equation of the Boost converter is linearized and then processed into a form under an ADRC framework:
Figure BDA0003468169380000105
wherein ,
Figure BDA0003468169380000111
ξ (t) represents the net perturbation of the internal and external perturbations of the system, whiley,
Figure BDA0003468169380000112
u,
Figure BDA0003468169380000113
Respectively representing the output voltage, a first derivative of the output voltage, a second derivative of the output voltage, and controlling the input duty cycle and the derivatives;
to improve observer efficiency, and alleviate observation pressure, the pole information is incorporated into an Extended State Observer (ESO), resulting in the following nominal equation:
Figure BDA0003468169380000114
wherein ,fnIs to include a total perturbation having a right half-plane, perturbing the portion fnThe right half-plane zero portion included therein is separated, as shown in equation 25,
Figure BDA0003468169380000115
wherein ,woIs observer bandwidth, s is Laplace operator, fζOther than the right half-plane zero.
In order to improve the effect of the right half-plane zero point, the influence of the right half-plane zero point is balanced by adding a filter; the designed filter is as follows:
Figure BDA0003468169380000116
let x1＝y,
Figure BDA0003468169380000117
The modified state equation is:
Figure BDA0003468169380000118
where g is assumed to be bounded but unknown;
the improved ESO is in the form of:
Figure BDA0003468169380000121
wherein
Figure BDA0003468169380000122
Respectively representing a part of the disturbance f observed by an extended observerζAnd the observed value of the system output x1 and its derivative x 2;
the system with disturbances is simplified to:
Figure BDA0003468169380000123
for simplicity in the form of equation 28, controller u is designed to:
Figure BDA0003468169380000124
the desired closed loop performance is achieved by selecting the feedback control:
Figure BDA0003468169380000125
based on bandwidth parameterization technique, respectively using wo and wcThe observer and controller bandwidths are shown. The number of parameters to be adjusted in the ADRC scheme is simplified by using a parametric observer and controller gain. Selecting observer gain betaa1＝3wo,βa2＝3wo 2,βa3＝wo 3And a controller gain k1＝wc 2,k2＝2wc。
Example 1
The control method is adopted to carry out control simulation on the Boost converter, and when the circuit parameters of the converter are shown in the table 1, the gains of the controller and the observer are selected to be wc＝500rad/s,wo＝4500rad/s。
Simulations of the voltage change from 5A to 10A (light to heavy) and 10A to 5A (heavy to light) resistance are shown in fig. 7 and 8, and the change in the dynamic process inductor current is shown in fig. 9. As can be seen from the above figures, the dynamic recovery time of the output voltage is about 6ms when the load is transitioned from 5A to 10A, and about 10ms when the load is transitioned from 10A to 5A.
Fig. 10 and 11 are simulation results of the original ADRC control method and the improved ADRC control method, respectively. FIG. 10 shows the voltage waveforms obtained using conventional ADRC control, with the times for the output voltage to reach steady state when the resistance changes from 5A to 10A (FIG. 10.a) and 10A to 5A (FIG. 10.b) being approximately 15ms and 10ms, respectively; fig. 11 shows the voltage waveforms obtained using conventional ADRC in combination with the digital time-optimized control proposed in this paper, the times for the output voltage to reach steady state when the resistance changes from 5A to 10A (fig. 11.a) and 10A to 5A (fig. 11.b) are approximately 15ms and 14ms, respectively. Therefore, as shown in fig. 9,10 and 11, the control method of the present invention has better dynamic response during load disturbance, and the ADRC controller improved by designing the filter has better compromise between dynamic response and closed-loop bandwidth.
TABLE 1
Parameter(s) Value of
Vcc 30V
Vo 50V
fs 100KHz
L 500μH
C 1000μF
D 0.4
R 50Ω
While the invention has been described with reference to specific embodiments, any feature disclosed in this specification may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise; all of the disclosed features, or all of the method or process steps, may be combined in any combination, except mutually exclusive features and/or steps.

Claims (6)

1.A digital optimal time dynamic control method of a Boost converter is characterized by comprising the following steps:
step 1, judging whether a circuit of a Boost converter is in a steady state or a transient state, and if the circuit is in the transient state, executing step 2; otherwise, executing step 5;
step 2, judging whether the load changes from heavy load to light load or from light load to heavy load, and if the load changes from light load to heavy load, executing the step 3; otherwise, executing step 4; the change from heavy load to light load is that the load current at the next moment is reduced compared with the load current at the current moment;
step 3, when the load jumps from light load to heavy load, at tonDuring the period, the switching tube is on and the duty ratio isAt t 100% >, atoffThe switching tube is turned off in the period, the duty ratio is 0%, and the shortest recovery time for the output voltage to reach the steady state again is tMRT，tMRT＝ton+toff；
wherein ,
Figure FDA0003468169370000011
in the above formula, Ion3For a load current at a known desired target operating point under heavy load iLn2The inductor current at the transient point, von2Output voltage at transient point, Vccn is normalized input voltage, iLntInductor current for heavy-duty operating points, iLn(0) The initial inductive current at the light load working point;
step 4, when the load jumps from heavy load to light load, at tonIn the period, the switching tube is switched on, and the duty ratio of the driving signal is 100%; at toffDuring the period, the switching tube is turned off, the duty ratio of the driving signal is 0%, and the shortest recovery time for the output voltage to reach the steady state again is tMRT，tMRT＝ton+toff，
wherein ,
Figure FDA0003468169370000012
in the above formula, iLn(0) For the initial value of the inductance current at the heavy-duty working point, iLntThe inductance current value V at the expected target operating point known during light loadccIs an input voltage vonAOutput voltage value v at inductor current 0 for turn-off traceonBOutput voltage value i at inductor current 0 for switching on traceon2Is the load current at the transient point;
and step 5, when the circuit is in a steady state, using an improved active disturbance rejection controller for control, wherein the active disturbance rejection controller is specifically,
Figure FDA0003468169370000013
in the above formula, k1 and k2For the controller gain, yrefIn order to achieve the desired output voltage,
Figure FDA0003468169370000014
respectively the output voltage and the inverse output voltage observed by the extended observer, b0In order to control the coefficients of the input,
Figure FDA0003468169370000015
is the estimated perturbation.
2. The digital optimal time dynamics control method of claim 1, wherein the topology of the Boost converter comprises: an inductor, a capacitor, a switching tube and a diode; the drain electrode of the switching tube is connected with one end of the inductor, and the source electrode of the switching tube is connected with the negative electrode of the input power supply; the anode of the diode is connected with one end of the inductor and the drain of the switching tube, the cathode of the diode is connected with one end of the output capacitor, and the other end of the output capacitor is connected with the negative electrode of the power supply.
3. The digital optimal time dynamics control method of claim 1, wherein the output voltage of the Boost converter cannot be negative.
4. The digital optimal time dynamics control method of claim 1, wherein the operating mode of the Boost converter during steady state is a continuous conduction mode.
5. The digital optimal time dynamics control method of claim 1, wherein the load disturbance causes the output voltage of the converter to be other than 0 regardless of a light load to load change or a load to light load change.
6. The method for digitally optimized time dynamics control according to claim 1, wherein the controller gain k1＝wc 2,k2＝2wc，wcA controller gain parameterized for bandwidth.
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